text: In atmospheric science, several different expressions for the Richardson number are commonly used: the flux Richardson number (which is fundamental), the gradient Richardson number, and the bulk Richardson number.
  * The flux Richardson number  is the ratio of buoyant production (or suppression) of turbulence kinetic energy to the production of turbulence by shear. Mathematically, this is:
  where  is the virtual temperature,  is the virtual potential temperature,  is the altitude,  is the  component of the wind,  is the  component of the wind, and  is the  (vertical) component of the wind. A prime (e.g. ) denotes a deviation of the respective field from its Reynolds average.
  * The gradient Richardson number  is arrived at by approximating the flux Richardson number using "K-theory". This results in:
  * The bulk Richardson number  results from making a finite difference approximation to the derivatives in the expression for the gradient Richardson number, giving:
  Here, for any variable , , i.e. the difference between  at altitude  and altitude . If the lower reference level is taken to be , then  (due to the no-slip boundary condition), so the expression simplifies to: